Why do cats hate other cats?

Cats don't hate each other in a general sense as the question implies. Domestic cats often live in multi-cat households and they often get along well or at the least tolerate each other. Feral cats often form colonies around a food source and get along under a hierarchy. So although all domestic cats are essentially solitary animals (as are wild cats) they are able to live in social groups when the conditions are right. Obviously if cats form a social group it must be the case that they don't hate each all the time and in general. Lions are the only wild cat that form groups  - prides. In this respect the domestic cat is similar to the lion.

Domestic cats live in groups around food sources such as at fish suppliers and restaurants etc. A desire to have a territory or home range will result in the domestic cat confronting intruders to their home range. This is usually a male unnuetered domestic cat. This gives the appearance of one cat hating another. It is more about maintaining a home range than actual hatred however.

Think about it. If a perfect stranger came into your house and set up home how would you feel towards that person?